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Emergent Criticality Through Adaptive Information Processing in Boolean Networks

By Alireza Goudarzi, Christof Teuscher, Natali Gulbahce and Thimo Rohlf


We study information processing in populations of Boolean networks with evolving connectivity and systematically explore the interplay between the learning capability, robustness, the network topology, and the task complexity. We solve a long-standing open question and find computationally that, for large system sizes $N$, adaptive information processing drives the networks to a critical connectivity $K_{c}=2$. For finite size networks, the connectivity approaches the critical value with a power-law of the system size $N$. We show that network learning and generalization are optimized near criticality, given task complexity and the amount of information provided threshold values. Both random and evolved networks exhibit maximal topological diversity near $K_{c}$. We hypothesize that this supports efficient exploration and robustness of solutions. Also reflected in our observation is that the variance of the values is maximal in critical network populations. Finally, we discuss implications of our results for determining the optimal topology of adaptive dynamical networks that solve computational tasks.Comment: 5 pages, 4 figure

Topics: Condensed Matter - Disordered Systems and Neural Networks, Computer Science - Neural and Evolutionary Computing, Nonlinear Sciences - Adaptation and Self-Organizing Systems
Year: 2012
DOI identifier: 10.1103/PhysRevLett.108.128702
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